For the backlighting of a display device, for example liquid crystal displays (LCDs), light emitting diodes can be used as radiation sources. However, such applications require a high gamut in order to be able to represent the greatest possible proportion of the colors perceptible to the human eye. By way of example, by means of LEDs that emit in the blue spectral range and a phosphor that emits in the yellow spectral range, radiation that appears white to the human eye can be generated with high efficiency, but with a reduced gamut. By adding further phosphors, the gamut can be improved but the efficiency decreases. A high color gamut can furthermore be achieved if three mutually different light emitting diodes directly generate radiation in the red, blue and green spectral ranges. However, this requires a complex electronic control on account of the driving of three individual colors.